Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-4y &= 3 \\ -3x-2y &= -1\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = 3x-1$ Divide both sides by $-2$ to isolate $y$ $y = {-\dfrac{3}{2}x + \dfrac{1}{2}}$ Substitute this expression for $y$ in the first equation. $-5x-4({-\dfrac{3}{2}x + \dfrac{1}{2}}) = 3$ $-5x + 6x - 2 = 3$ Simplify by combining terms, then solve for $x$ $1x - 2 = 3$ $1x = 5$ $x = 5$ Substitute $5$ for $x$ back into the top equation. $-5( 5)-4y = 3$ $-25-4y = 3$ $-4y = 28$ $y = -7$ The solution is $\enspace x = 5, \enspace y = -7$.